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There is, I feel, rather a bit of a difference between real-world kings (who were really only different by virtue of their title, which could have been given to anyone else, regardless of worth) and an alicorn who is physically different.
We don't know if being an alicorn actually grants any kind of special power, other than possibly a political status and power, and Twilight certainly has plenty of actual power and potential without arbitrarily being given wings or a title.
I wouldn't want Applejack to suddenly sprout wings and become a pegasus either. Not permanently, at least. Not because I object to Applejack being granted power, but because I feel it cheapens being a pegasus if any earth pony could theoretically be turned into one through some magic ritual. Bam! Pegasus! Down with the boring old earth ponies.
Frankly that'd cheapen earth ponies too. I mean, so it's better to be a pegasus? Applejack is not good enough as she is? Or, in this case, so it's so much better to be an alicorn rather than a regular unicorn? Why is it not great enough that Twilight's is a pretty unique and special unicorn?
What I say is, Twilight has power and is great the way she is, she doesn't need to become an alicorn to be special, and she doesn't need to become a princess either. In fact, I feel it takes away from her character if she's destined to just become another pretty pony princess because that's the destiny and dream of every great unicorn, isn't it? Bah, humbug to that!
Twilight should stand out, she should be unique and special on her own terms. Just like not every woman's dream should be to land a rich and handsome husband, right? Not every unicorn's dream should be to become a princess.
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As for the second point, I'm not saying she'd become aloof or that her friends would start hating her guts or be jealous of her. I'm sure it's quite possible that they'd be happy for her, and that she would find time to still be with them and all.
My objection is from an outside point of view, from our point of view, not from Twilight's. I feel it would change the mood and feeling of the show if the characters were changed so fundamentally. I probably would like RD to not become a Wonderbolt either, at least during the show. I mean, I hope she will be one day, but I don't want the show to suddenly be about Princess Twilight and her old friends, one of which is a famous Wonderbolt.
I want them to stay simple ponies, simple friends, unique in their own ways, while the show lasts. Any future they have should stay indefinitely in the future, from our point of view, if you see what I'm trying to say.